OK, excellent answer. But what if every flip is an unfair toss. Market is 50/51 but 20,000,000/1,000. Still a flip at 50/51, but definitely not fair, and certainly not fair between 49 and 52. Modeling it makes no difference, I don't trust those things much anyway. Just something I've been pondering lately.
The binomial model converges to the same result with far more parsimony than any continuous ito calculus derived solution. More importantly the binomial model is computationally tractable and doesn't rely on the discretization of an SPDE which is subject to some error as a result of the translation from continuous to discrete space. Only a rube would prefer complicated and obscure to simple and straightforward. But whatever makes you feel smarter, I guess.
Really? I traded and structured exotic rates derivatives at several sell side banks for years. How come continuous stochastic models were used throughout, such as the SABR model? Has nothing to do with smarter. You talked out of your ass without knowing at all what market practitioners use. Even for vanilla derivatives or barriers, binomial model are hardly ever used. Your claim that binomial models are used for pricing is flat out wrong. Dude, I like some of your content but hell, when you get riled up about certain social issues that someone may disagree with you (as in another thread) , you get all fired up and aim bazookas at the messenger. Not that I care, I have a very thick skin. But it would help to stay factual in this thread. Fact is that market practitioners use other discretizations than the binomial model.
None of the pricing models are scientifically absolutely accurate. For continuous pricing the log normality distributional assumption is not accurate but has very nice mathematical properties for random variable transformations and change of risk measures.
I made a long post but I think I can summarize this in a few sentences: 1. You didn't understand what I meant by discretizing the SPDE which is the only way to make a stochastic partial differential equation (the BSM) tractable for computation. 2. I didn't say anything about the SABR model and I know nothing about it 3. The binomial option pricing model is slower but more accurate in almost every case you'd use the BSM for. 4. The binomial option pricing model is more flexible for exotics. It's cute you think I'm not being factual. If you clicked the link I posted you would've read all of this and saved yourself the 5 minutes it took you to type this ill thought out response. But hey, it seems I struck a nerve with you. I guess this was you just venting at me.
i think many of of us can show trades,in historical charts, based on pattern/s, which would have worked a hundred times. it does not matter whether, i or anyone else, made money trading these because this thread is not about money being made. it is about market being random or not and this clearly shows that market is not random and money can be made, if you are willing to wait for these patterns.
but even if the market is random it does not mean that the odds are indeterminable .......it just means that they are 1:1.........
If I throw a ball 10 times into a basket does that mean on the 11th time it will make it in - or is it some function of probability - the environment (market noise), my mentality (strategy), and my team (market sentiment)? It's foolish to say what you are saying. Why is it foolish? Apophenia is the term. Humans are fundamentally incapable of determining real patterns from an imagined ones in any general case. How do you think you get people who believe the moon has some effect on the market! The gamblers fallacy is a popular explanation for people "being sure something will happen" after some event in the past. Indeterminable odds are not 1:1. Indeterminable odds are indeterminable. Enlightenment is realizing you are gambling and playing a game of probabilities - foolishness lies in pretending any pattern has any fundamental absolute meaning. There is significant difference in saying "when X, there is a 45% chance of event Y happens" and "because I saw a bearish engulfing pattern Y will happen".